2] RELATION TO THE MOTION OF THE NODE OF THE MOON'S ORBIT. 99 

 Each of such terms will be of the form 



_ _ 



L(y +P - 1 Y - <] [(y +pY - O [(y +p + 1) 2 - *' : ] 



where both s and s+1 are integers other than p 1, p, p+l. Now 

 we have 



a- 



[(j + s) y ~ "] [(7 + * + I) 2 - K-"] q (<f - 

 Hence the sum will be 



- 2a'b . 



_1 



We find this latter sum 



Substitute for B its value A' + TrcotqirA, and we find the terms 

 of the determinant 



(33} nd i*ti-*bA 32 (35^-280^ + 497g-- 108)] 



(33) and (34) - a M j^_ W _ 4 ) g (g - 1)^ (^ - 4)^ ( 3 2 - 9) / ' 



the terms in A* cancelling one another. 



In this formula it may be shewn that q I appears in only the first 

 power in the denominator. 



Next consider the term (8), 321. 



132 



